2. Chapter Modern Portfolio Theory

• The assumption is that investors makes investment decisions based on two parameters

• return and risk (volatility)

A rational investor would only invest in:

• a portfolio that has the highest expected return for a given risk level (volatility) respectively

• A portfolio that has the lowest risk level (volatility) for a given expected return (efficient portfolio)

• efficient frontier

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• if a risk free asset is available (for example a german state bond) the efficient frontier is a traight line and is called the capital market line

• Diversification is only usefull when the correlation between the assets is below one. Otherwise no efficient frontier is possible

• the trick is that you can change many thing so that bonds or shares have a relativ low correlation, for example:

  • issuer

  • maturity

  • industries

  • sectors

  • countries

    
    

• portfolio, consisting of several investments with correlations lower than one, is more efficient than a portfolio consisting only of two investments.

• Estimate the expected return and the volatility for each single investment

• estimate the correlations

• Determine the efficient portfolios (efficient frontier)

• Choose one of the efficient portfolios

• That fits the utility funtion of the investor

• That offers the highest return for a level of risk targeted by the investor

• that offers the lowest level of risk for a targeted return

• the investor does ot need all the portfolio for his decision on the efficient frontier

• he even does not need any return expectations

• he implicitly is minimizing the risk and accepting the resulting expected return

• investing in a sufficient large number of different investments with equal weightings (weighting = 1/n) and positive correlated returns

• This means, a naive diversified portfolio with many investments has approximately the same risk as the market portfolio

• The basic idea is to explain the return of each single asset (stock etc.) with its relationship to the return of an index

• beta factor of 1 means the portfolio the same risk as the index

• beta factor is smaller than 1 means the portfolio is less sensitive to the index

• beta factor is bigger than 1 means the portfolio is more sensitive to the index

• Alpha: is the specific constant

• Beta: measuring the sensitivity of the asset‘s return to fluctuations in the index‘s return

• e(asset): summarizing all variable (i.e. random) return components that cannot be explained by the common factor (the index return)